最长k可重区间集问题【网络流24题】

  1 #include <bits/stdc++.h>
  2 #define dbg(x) cout << #x << "=" << x << endl
  3 #define eps 1e-8
  4 #define pi acos(-1.0)
  5 
  6 using namespace std;
  7 typedef long long LL;
  8 const int maxn = 1e5 +7;
  9 const int inf  = 0x3f3f3f3f;
 10 
 11 int n, m, s, t;
 12 int head[maxn],pre[maxn],inq[maxn],dis[maxn];
 13 int a[maxn];
 14 int cnt = 1;
 15 int path[2][maxn];
 16 int mincost = 0, maxflow = 0;
 17 struct edge {
 18     int u,to,nxt,w,c;
 19 }e[maxn << 1];
 20 int tot[5];
 21 
 22 template<class T>inline void read(T &res)
 23 {
 24     char c;T flag=1;
 25     while((c=getchar())<‘0‘||c>‘9‘)if(c==‘-‘)flag=-1;res=c-‘0‘;
 26     while((c=getchar())>=‘0‘&&c<=‘9‘)res=res*10+c-‘0‘;res*=flag;
 27 }
 28 
 29 inline void BuildGraph(int u, int v, int w, int cost)
 30 {
 31     e[++cnt] = (edge){u, v, head[u], w,  cost}, head[u] = cnt;
 32     e[++cnt] = (edge){v, u, head[v], 0, -cost}, head[v] = cnt;///反向边
 33 }
 34 
 35 queue<int> q;
 36 
 37 inline void init() {
 38     memset(head, 0, sizeof(head));
 39     memset(pre, 0, sizeof(pre));
 40     memset(inq, 0, sizeof(inq));
 41     memset(dis, 0, sizeof(dis));
 42     memset(e, 0, sizeof(e));
 43     while(!q.empty()) {
 44         q.pop();
 45     }
 46     mincost = maxflow = 0;
 47     cnt = 1;
 48 }
 49 
 50 bool SPFA(int x)
 51 {
 52     memset(inq, 0, sizeof(inq));
 53     for(int i = s; i <= t; i++) {
 54         dis[i] = inf;
 55     }
 56     q.push(x);
 57     dis[x] = 0;
 58     inq[x] = 1;
 59     while(!q.empty()) {
 60         int u = q.front();
 61         q.pop();
 62         inq[u] = 0;
 63         for(int i = head[u]; i; i = e[i].nxt) {
 64             int v = e[i].to, w = e[i].c;
 65             if(e[i].w > 0) {
 66                 if(dis[u] + w < dis[v]) {
 67                     dis[v] = dis[u] + w;
 68                     pre[v] = i;
 69                     if(!inq[v]) {
 70                         q.push(v);
 71                         inq[v] = 1;
 72                     }
 73                 }
 74             }
 75         }
 76     }
 77     if(dis[t] == inf)
 78         return 0;
 79     return 1;
 80 }
 81 
 82 void MCMF()
 83 {
 84     while(SPFA(s)) {
 85         int temp = inf;
 86         for(int i = pre[t]; i; i = pre[e[i].u]) {
 87             temp = min(temp, e[i].w);
 88         }
 89         for(int i = pre[t]; i; i = pre[e[i].u]) {
 90             e[i].w   -= temp;
 91             e[i^1].w += temp;
 92             mincost += e[i].c * temp;
 93             //printf("e[%d].c:%d\n",i, e[i].c);
 94             //printf("ans:%d\n",ans);
 95         }
 96         //maxflow += temp;
 97     }
 98 }
 99 
100 int k;
101 int l[maxn], r[maxn];
102 int ls[maxn], lss[maxn];
103 int totls, totlss;
104 int len[maxn];
105 
106 void Unique() {
107     for ( int i = 1; i <= n; ++i ) {
108         for ( int j = 1; j <= totlss; ++j ) {
109             if(l[i] == lss[j]) {
110                 l[i] = j;
111             }
112             if(r[i] == lss[j]) {
113                 r[i] = j;
114             }
115         }
116     }
117 }
118 
119 int main()
120 {
121     //freopen("data.txt", "r", stdin);
122     read(n); read(k);
123     init();
124     for ( int i = 1; i <= n; ++i ) {
125         read(l[i]); read(r[i]);
126         ls[++totls] = l[i];
127         ls[++totls] = r[i];
128         len[i] = r[i] - l[i];
129     }
130     sort(ls + 1, ls + 1 + totls);
131     for ( int i = 1; i <= totls; ++i ) {
132         if(ls[i] == ls[i-1])
133             continue;
134         lss[++totlss] = ls[i];
135     }
136     Unique();
137     s = 0;
138     for ( int i = 1; i <= n; ++i ) {
139         t = max(t, r[i]);
140         BuildGraph(l[i], r[i], 1, -len[i]);
141     }
142     for ( int i = 0; i <= t; ++i ) {
143         BuildGraph(i, i + 1, k, 0);
144     }
145     ++t;
146     MCMF();
147     cout << -mincost << endl;
148     return 0;
149 }